Question 1129226


What is the average rate of change of {{{f(x)=x^3-3x+2}}} from{{{ -8}}} to {{{-6}}}, {{{-2}}} to {{{2}}}, {{{2 }}}to{{{ 8}}} 

{{{f(-8)=(-8)^3-3(-8)+2}}}

{{{f(-8)=-512+24+2}}}

{{{f(-8)=-486}}}


{{{f(-6)=(-6)^3-3(-6)+2}}}

{{{f(-6)=-216+18+2}}}

{{{f(-6)=-196}}}

the average rate of change from {{{-8}}} to {{{-6}}} is:

Given a function f(x) plotted in the Cartesian plane as {{{y = f(x)}}}, the average rate of change (or average rate of change function) of {{{f}}} from {{{x}}} to {{{a}}} is given by


{{{A}}}({{{x}}},{{{ a}}}) = {{{(f(x) - f(a))/(x - a)}}}=>{{{x=-8}}} and {{{a=-6}}}

since {{{f(-8)=-486}}} and {{{f(-6)=-196}}}, we have

{{{A}}}({{{-8}}},{{{ -6}}}) = {{{(-486 - (-196))/(-8 - (-6))}}}

{{{A}}}({{{-8}}},{{{ -6}}}) = {{{(-486 +196)/(-8 +6)}}}

{{{A}}}({{{-8}}},{{{ -6}}}) = {{{(-290)/(-2)}}}

{{{A}}}({{{-8}}},{{{ -6}}}) = {{{145}}}


{{{f(-2)=(-2)^3-3(-2)+2}}}

{{{f(-2)=-8+6+2}}}

{{{f(-2)=0}}}


{{{f(2)=2^3-3(2)+2}}}

{{{f(2)=8-6+2}}}

{{{f(2)=4}}}

the average rate of change from {{{-2}}} to {{{2}}} is:

{{{A}}}({{{-2}}},{{{ 2}}}) = {{{(0 - 4)/(-2 - 2)}}}
{{{A}}}({{{-2}}},{{{ 2}}}) = {{{( - 4)/(-4)}}}

{{{A}}}({{{-2}}},{{{ 2}}}) = {{{1}}}



{{{f(2)=2^3-3(2)+2}}}

{{{f(2)=8-6+2}}}

{{{f(2)=4}}}


{{{f(8)=8^3-3(8)+2}}}

{{{f(8)=512-24+2}}}

{{{f(8)=490}}}



the average rate of change from {{{2}}} to {{{8}}} is:

{{{A}}}({{{2}}},{{{ 8}}}) = {{{(4 - 490)/(2 - 8)}}}

{{{A}}}({{{2}}},{{{ 8}}}) = {{{( - 486)/( - 6)}}}

{{{A}}}({{{2}}},{{{ 8}}}) = {{{81}}}